scipy.signal.unique_roots(p, tol=0.001, rtype='min')[source]#

Determine unique roots and their multiplicities from a list of roots.


The list of roots.

tolfloat, optional

The tolerance for two roots to be considered equal in terms of the distance between them. Default is 1e-3. Refer to Notes about the details on roots grouping.

rtype{‘max’, ‘maximum’, ‘min’, ‘minimum’, ‘avg’, ‘mean’}, optional

How to determine the returned root if multiple roots are within tol of each other.

  • ‘max’, ‘maximum’: pick the maximum of those roots

  • ‘min’, ‘minimum’: pick the minimum of those roots

  • ‘avg’, ‘mean’: take the average of those roots

When finding minimum or maximum among complex roots they are compared first by the real part and then by the imaginary part.


The list of unique roots.


The multiplicity of each root.


If we have 3 roots a, b and c, such that a is close to b and b is close to c (distance is less than tol), then it doesn’t necessarily mean that a is close to c. It means that roots grouping is not unique. In this function we use “greedy” grouping going through the roots in the order they are given in the input p.

This utility function is not specific to roots but can be used for any sequence of values for which uniqueness and multiplicity has to be determined. For a more general routine, see numpy.unique.


>>> from scipy import signal
>>> vals = [0, 1.3, 1.31, 2.8, 1.25, 2.2, 10.3]
>>> uniq, mult = signal.unique_roots(vals, tol=2e-2, rtype='avg')

Check which roots have multiplicity larger than 1:

>>> uniq[mult > 1]
array([ 1.305])